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   "cell_type": "code",
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   "source": [
    "%matplotlib inline\n",
    "import torch\n",
    "import tqdm\n",
    "import torch.nn as nn\n",
    "from d2l import torch as d2l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "61d2c4bf",
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   ],
   "source": [
    "T = 1000\n",
    "time = torch.arange(1, T + 1, dtype=torch.float32)\n",
    "X = torch.sin(0.01 * time) + torch.normal(0, 0.2, (T, )) # 综上所述，(T,) 和 (T, -1) 都表示一维张量，区别在于对于 (T, -1)，系统会根据其他维度自动计算该维度的大小。\n",
    "d2l.plot(time, [X], 'time', 'x', xlim=[1, 1000], figsize=(6, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b8dfd160",
   "metadata": {},
   "outputs": [],
   "source": [
    "tau = 4\n",
    "features = torch.zeros(T - tau, tau)\n",
    "for i in range(tau):\n",
    "    features[:, i] = X[i: T - tau + i]\n",
    "labels = X[tau:].reshape(-1, 1)\n",
    "\n",
    "batch_size, n_train = 16, 600\n",
    "train_iter = d2l.load_array((features[: n_train], labels[: n_train]), batch_size, is_train=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bf057fb2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def init_weight(m):\n",
    "    if isinstance(m, nn.Linear):\n",
    "        nn.init.xavier_uniform_(m.weight) \n",
    "\n",
    "def get_net():\n",
    "    net = nn.Sequential(\n",
    "        nn.Linear(4, 10),\n",
    "        nn.ReLU(),\n",
    "        nn.Linear(10, 1)\n",
    "    )\n",
    "    net.apply(init_weight)\n",
    "    return net\n",
    "\n",
    "loss = nn.MSELoss(reduction='none')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ff05e8f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(net, train_iter, loss, epochs, lr):\n",
    "    trainer = torch.optim.Adam(net.parameters(), lr)\n",
    "    for epoch in range(epochs):\n",
    "        for X, y in train_iter:\n",
    "            trainer.zero_grad()\n",
    "            l = loss(net(X), y)\n",
    "            l.sum().backward()\n",
    "            trainer.step()\n",
    "        print(f'epoch {epoch + 1}, '\n",
    "              f'loss: {d2l.evaluate_loss(net, train_iter, loss):f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "61be1146",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1, loss: 0.056275\n",
      "epoch 2, loss: 0.049737\n",
      "epoch 3, loss: 0.049516\n",
      "epoch 4, loss: 0.049448\n",
      "epoch 5, loss: 0.048946\n",
      "epoch 6, loss: 0.048468\n",
      "epoch 7, loss: 0.047777\n",
      "epoch 8, loss: 0.047624\n",
      "epoch 9, loss: 0.049080\n",
      "epoch 10, loss: 0.048601\n"
     ]
    }
   ],
   "source": [
    "net = get_net()\n",
    "train(net, train_iter, loss, 10, 0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "11e53d37",
   "metadata": {},
   "outputs": [
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   "source": [
    "onestep_preds = net(features)\n",
    "d2l.plot([time, time[tau:]],\n",
    "         [X.detach().numpy(), onestep_preds.detach().numpy()], 'time',\n",
    "         'x', legend=['data', '1-step preds'], xlim=[1, 1000],\n",
    "         figsize=(6, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2a1385c8",
   "metadata": {},
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   "source": [
    "multistep_preds = torch.zeros(T)\n",
    "multistep_preds[: n_train + tau] = X[: n_train + tau]\n",
    "for i in range(n_train + tau, T):\n",
    "    multistep_preds[i] = net(\n",
    "        multistep_preds[i - tau:i].reshape((1, -1)))\n",
    "    \n",
    "d2l.plot([time, time[tau:], time[n_train + tau:]],\n",
    "         [X.detach().numpy(), onestep_preds.detach().numpy(),\n",
    "          multistep_preds[n_train + tau:].detach().numpy()], 'time',\n",
    "         'x', legend=['data', '1-step preds', 'multistep preds'],\n",
    "         xlim=[1, 1000], figsize=(6, 3))"
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  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1fe366aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "max_steps = 64\n",
    "\n",
    "features = torch.zeros((T - tau - max_steps + 1, tau + max_steps))\n",
    "# 列i（i<tau）是来自x的观测，其时间步从（i）到（i+T-tau-max_steps+1）\n",
    "for i in range(tau):\n",
    "    features[:, i] = X[i: i + T - tau - max_steps + 1]\n",
    "\n",
    "# 列i（i>=tau）是来自（i-tau+1）步的预测，其时间步从（i）到（i+T-tau-max_steps+1）\n",
    "for i in range(tau, tau + max_steps):\n",
    "    features[:, i] = net(features[:, i - tau:i]).reshape(-1)"
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  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0ab41fd5",
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
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     "metadata": {},
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   ],
   "source": [
    "steps = (1, 4, 16, 64)\n",
    "d2l.plot([time[tau + i - 1: T - max_steps + i] for i in steps],\n",
    "         [features[:, (tau + i - 1)].detach().numpy() for i in steps], 'time', 'x',\n",
    "         legend=[f'{i}-step preds' for i in steps], xlim=[5, 1000],\n",
    "         figsize=(6, 3))"
   ]
  }
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